User jackie boy - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T20:37:54Z http://mathoverflow.net/feeds/user/4043 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/16917/what-is-a-reference-for-profinite-sets What is a reference for profinite sets? jackie boy 2010-03-02T20:59:20Z 2012-06-06T15:47:07Z <p>The question is in the title. The motivation behind the question is as follows: there are plenty of references about profinite groups and profinite completions of groups. It seems that their not exactly a wealth of references about profinite sets and profinite completions of sets.</p> http://mathoverflow.net/questions/49546/a-question-about-the-adjointness-of-two-functors-on-presheaf-categories-induced-b A question about the adjointness of two functors on presheaf categories induced by a functor on small categories jackie boy 2010-12-15T17:21:29Z 2010-12-15T17:59:22Z <p>Given any functor between two small categories, one may construct two functors between their presheaf categories. Let $f:\mathcal{A}\rightarrow\mathcal{B}$ be such a functor. Then we may extend this functor to a functor, $f_{\ast}: \hat{\mathcal{A}} \rightarrow \hat{\mathcal{B}}$ by co-continuity. On the other hand we have a functor, $f^{\ast}:\hat{\mathcal{B}}\rightarrow\hat{\mathcal{A}}$ defined by the composite, i.e., by taking $X \mapsto X \circ f^{op}$. My question is: are these two functors adjoint?</p> http://mathoverflow.net/questions/22676/terminology-about-ring-algebra-in-abstract-algebra-and-measure-theory/34322#34322 Answer by jackie boy for terminology about ring/algebra in abstract algebra and measure theory jackie boy 2010-08-03T03:17:52Z 2010-08-03T03:17:52Z <p>For what it's worth, a ring is an algebra over the integers.</p> http://mathoverflow.net/questions/1861/looking-for-an-introduction-to-orbifolds/15545#15545 Answer by jackie boy for Looking for an introduction to orbifolds jackie boy 2010-02-17T02:59:53Z 2010-02-17T02:59:53Z <p>A word of warning: the "paths" on an orbifold are subtle.</p> http://mathoverflow.net/questions/8608/simplicial-homotopy-book-suggestion-for-htt-computations/15541#15541 Answer by jackie boy for Simplicial homotopy book suggestion for HTT computations jackie boy 2010-02-17T02:39:31Z 2010-02-17T02:39:31Z <p>One thing that might help is to develop some intuition about triangulable spaces and the analogies with simplicial sets. Taking the geometric realization and drawing some pictures might hel you get comfortable with these ideas.</p> http://mathoverflow.net/questions/14830/which-graphs-are-cayley-graphs/15531#15531 Answer by jackie boy for Which graphs are Cayley graphs? jackie boy 2010-02-17T01:31:09Z 2010-02-17T01:31:09Z <p>Conjecture: Let (V,E) be a directed graph such that 1. The in degree of each edge is equal to the out degree of each edge and each vertex has the same in and out degrees. Then this graph is a cayley graph. Maybe this isn't quite right, but some fiddling of these conditions will be equivalent to having a cayley graph.</p> http://mathoverflow.net/questions/49546/a-question-about-the-adjointness-of-two-functors-on-presheaf-categories-induced-b Comment by jackie boy jackie boy 2010-12-15T17:24:01Z 2010-12-15T17:24:01Z I appologize about the terrible formatting job. http://mathoverflow.net/questions/16917/what-is-a-reference-for-profinite-sets/16929#16929 Comment by jackie boy jackie boy 2010-03-03T06:03:58Z 2010-03-03T06:03:58Z What I am calling the profinite completion of a set is almost the same as for a group, except everytime the word group is used, you replace it the with the word set. Now the Stone Cech compactifaication of a (discrete) space misses the words, &quot;totally disconnected&quot;. Wikipedia states (so a grain of salt) that the stone cech compactification happens to be totally disconnected. So ths notion of profinite completion seems to be the stone cech compactification. I would like to make a remark on the terminology. Any concrete category with filtered limits has a &quot;profinite completion&quot; functor. http://mathoverflow.net/questions/16917/what-is-a-reference-for-profinite-sets Comment by jackie boy jackie boy 2010-03-02T22:02:17Z 2010-03-02T22:02:17Z The projective limit definition would amount to the same thing. http://mathoverflow.net/questions/16917/what-is-a-reference-for-profinite-sets Comment by jackie boy jackie boy 2010-03-02T22:01:11Z 2010-03-02T22:01:11Z Let us first say what a profinite set is. This is a compact Haussdorf totally disconnected topological space. We may form the category of profinite spaces where the morphisms are continuous maps between them. Their is a forgetfull functor from profinite sets to sets that forgets the topology. Profinite completion is the left adjoint to this functor.